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author | Chantal Keller <Chantal.Keller@lri.fr> | 2021-04-26 18:27:37 +0200 |
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committer | Chantal Keller <Chantal.Keller@lri.fr> | 2021-04-26 18:27:37 +0200 |
commit | cdadc5d338e3c00c4cd22a3a3d7197f71d4d7a44 (patch) | |
tree | 66697deb3845810897976e1eecbb5b88ad2bab09 /src | |
parent | 39b4d1d31c6446c937164039cac585dbe91b8b29 (diff) | |
download | smtcoq-cdadc5d338e3c00c4cd22a3a3d7197f71d4d7a44.tar.gz smtcoq-cdadc5d338e3c00c4cd22a3a3d7197f71d4d7a44.zip |
Equality between Booleans should be changed for hypotheses
Diffstat (limited to 'src')
-rw-r--r-- | src/PropToBool.v | 14 | ||||
-rw-r--r-- | src/QInst.v | 43 |
2 files changed, 53 insertions, 4 deletions
diff --git a/src/PropToBool.v b/src/PropToBool.v index 64d88cf..8dc970f 100644 --- a/src/PropToBool.v +++ b/src/PropToBool.v @@ -42,12 +42,16 @@ Ltac prop2bool := | [ |- context[ Z.ge _ _ ] ] => rewrite <- geb_ge | [ |- context[ Z.eq _ _ ] ] => rewrite <- Z.eqb_eq - | [ |- context[ @Logic.eq ?t _ _ ] ] => + | [ |- context[ @Logic.eq ?t ?x ?y ] ] => lazymatch t with | bitvector _ => rewrite <- bv_eq_reflect | farray _ _ => rewrite <- equal_iff_eq | Z => rewrite <- Z.eqb_eq - | bool => fail + | bool => + lazymatch y with + | true => fail + | _ => rewrite <- eqb_true_iff + end | _ => lazymatch goal with | [ p: (CompDec t) |- _ ] => @@ -107,6 +111,8 @@ Ltac bool2prop_true := | [ |- context[ Z.geb _ _ ] ] => rewrite geb_ge | [ |- context[ Z.eqb _ _ = true ] ] => rewrite Z.eqb_eq + | [ |- context[ Bool.eqb _ _ = true ] ] => rewrite eqb_true_iff + | [ |- context[ eqb_of_compdec ?p _ _ = true ] ] => rewrite <- (@compdec_eq_eqb _ p) | [ |- context[ ?G0 || ?G1 = true ] ] => @@ -218,6 +224,7 @@ Section Test. Hypothesis basic : forall (l1 l2:list A), length (l1++l2) = length l1 + length l2. Hypothesis no_eq : forall (z1 z2:Z), (z1 < z2)%Z. Hypothesis uninterpreted_type : forall (a:A), a = a. + Hypothesis bool_eq : forall (b:bool), negb (negb b) = b. Goal True. Proof. @@ -225,12 +232,13 @@ Section Test. prop2bool_hyp no_eq. prop2bool_hyp uninterpreted_type. admit. + prop2bool_hyp bool_eq. prop2bool_hyp plus_n_O. Abort. Goal True. Proof. - prop2bool_hyps (basic, plus_n_O, no_eq, uninterpreted_type, plus_O_n). + prop2bool_hyps (basic, plus_n_O, no_eq, uninterpreted_type, bool_eq, plus_O_n). admit. Abort. End Test. diff --git a/src/QInst.v b/src/QInst.v index 4ebdcc9..4a4ddc2 100644 --- a/src/QInst.v +++ b/src/QInst.v @@ -29,7 +29,7 @@ Qed. Hint Resolve impl_split. -(* verit silently transforms an <implb (a || b) c> into a <or (not a) c> +(** verit silently transforms an <implb (a || b) c> into a <or (not a) c> or into a <or (not b) c> when instantiating such a quantified theorem *) Lemma impl_or_split_right a b c: implb (a || b) c = true -> negb b || c = true. @@ -45,6 +45,35 @@ Proof. destruct a; destruct c; intuition. Qed. +(** same for Boolean equivalence, modulo symmetry *) +Lemma eqb_sym_or_split_right a b c: + Bool.eqb c (a || b) = true -> negb b || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + +Lemma eqb_sym_or_split_left a b c: + Bool.eqb c (a || b) = true -> negb a || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + +Lemma eqb_or_split_right a b c: + Bool.eqb (a || b) c = true -> negb b || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + +Lemma eqb_or_split_left a b c: + Bool.eqb (a || b) c = true -> negb a || c = true. +Proof. + intro H. + destruct a; destruct c; intuition. +Qed. + (** verit considers equality modulo its symmetry, so we have to recover the right direction in the instances of the theorems *) (* TODO: currently incomplete *) @@ -159,6 +188,18 @@ Ltac vauto := | eapply impl_or_split_left; first [ strategy1 H | strategy2 H ] + | eapply eqb_sym_or_split_right; + first [ strategy1 H + | strategy2 H ] + | eapply eqb_sym_or_split_left; + first [ strategy1 H + | strategy2 H ] + | eapply eqb_or_split_right; + first [ strategy1 H + | strategy2 H ] + | eapply eqb_or_split_left; + first [ strategy1 H + | strategy2 H ] ] end ] |